In a scanning probe microscope, such as a scanning tunneling microscope (SPM), a scanning near-field optical microscope (SNOM) or an atomic force microscope (AFM), for example, a probe is scanned across the surface of a sample to determine properties of the surface such as topography or magnetic field strength, so that these properties can be displayed for viewing. Alternately, the sample can be scanned across a fixed probe. Some of these microscopes, i.e., the SPM and the AFM, have been constructed with the ability to resolve individual atoms by either scanning the probe or the sample. The scanner which provides the motion is usually a piezoelectric device adapted for moving in all three dimensions, i.e. in the X-Y plane and in the vertical (Z-axis) direction. As can be appreciated, if one is to resole movement of a probe to the atomic level, the actuating mechanism must be stable and accurately moveable in small increments.
Three dimensional scanners have been made in the form of a tube whose probe-or sample-carrying end can be made to deflect in the X,Y and Z directions through the application of voltages to various electrodes on the tube. As depicted in simplified form in FIGS. 1 and 2, the scanner 10 has a plurality of electrodes (not shown) to which voltages are applied to cause scanning action. The core of the scanner 10 is formed from a tube of a piezoelectric material. The scanner 10 is attached to a structure at 12 and has a free end at 14 to which the probe 16 (or sample) is attached. By applying a voltage to certain electrodes, the scanner 10 can be made to elongate and shorten, as indicated by the dashed arrows, and thereby create motion in the Z-axis. Likewise, by applying a voltage to other electrodes, the scanner 10 can be made to deflect the free end 14 to one side or the other, or both, and thereby create motion in the X-and Y-axes as indicated by the ghosted positions of FIG. 1 and 2. As those skilled in the art will readily recognize, a variety of other scanner configurations (tripods, bimorph benders, flexure stages, etc.) and materials (electrostrictive, etc.) can be used within the scope and spirit of the present invention, even though the above background description refers to piezoelectric tube scanners.
With acceptance and contemporary usage of such devices, it has become important to make scanning probe microscopes which have large scan ranges (for example, up to 150 microns) and good mechanical stability. The motion of the piezoelectric scanner is essentially proportional to the electric field in the piezoelectric material, which is equal to the voltage across the material divided by the thickness of the tube. As is known in the art, complementary voltages x, -x and y, -y can be applied to the various scanning electrodes to give larger scan ranges and more symmetry. While such techniques can provide the larger scan range of movement desired, the inherent nature of the piezoelectric material used to form the tubes begins to create problems of its own as the scan distance (i.e. the amount of bending created in the tube) is increased.
Scanning is typically accomplished in a so-called "raster" fashion such as that of the electron beam which creates a television picture; that is, the probe 16 (or sample) moves in, for example, the X direction at a high rate, and in the perpendicular direction, i.e. the Y direction, at a low rate to trace out a path such as that indicated as 28 in FIG. 3. Data about the height, magnetic field, temperature, etc. of the surface 30 of the sample 18 is then collected as the probe 16 is moved along. In these scanners, the X and Y position of the probe 16 is inferred from the voltages which are applied to the electrodes on the piezoelectric material of the tube. In the prior art, these scan voltages are sometimes triangle functions in X and Y (vs. time) to produce, if the deflection of the scanner is linear with voltage, a raster scan of the probe in both the X and Y directions. Often, DC voltages are also added to the scan electrodes to position the raster scan over different areas of the sample surface; that is, to select where on the sample the center position of the raster scan will be. The triangle function has the feature that the voltage, and therefore presumably the probe position, changes at a constant rate so that the probe moves at a constant velocity back and forth in the X direction, while moving at a lower constant velocity up and down in the Y direction. This constant velocity then allows data taken at constant time intervals (as the probe moves in X and Y) to also be spaced at constant distance intervals. Since computers can conveniently take data at constant time intervals, they can then store and/or plot the data in a two-dimensional array representing position, i.e. in an X-Y array. It will be appreciated by those skilled in the art that the motion in X and Y will usually consist of small steps rather than a linear ramp because the scan voltages are changed in finite increments, as is convenient under computer control.
As the field of scanning probe microscopes has progressed and larger scans of up to 150 microns have been produced so that, for example, the properties of manufactured objects such as optical disks and magnetic recording heads can be measured, the inherent properties of the piezoelectric materials employed in the tubes has begun to affect the above-described scanning process adversely. This is because, unfortunately, piezoelectric material, especially that of high sensitivity, is not a linear material; that is, the deflection of the material is not linear with the voltage applied to the electrodes. Also, the material exhibits hysteresis so that reversals in the direction in which the voltage is changing do not produce a proportional reversal in the direction in which the position of the probe changes. Thus, a triangular voltage in time applied to the electrodes on the piezoelectric material in the manner of the prior art as described above does not produce a linear scan in time. This is illustrated in FIG. 4, where the position of a probe on the scanner as a function of the driving voltage for a one dimensional scan is graphed in simplified form. Notice that as the direction of the voltage changes at the ends of the scan, the position does not trace out the same path. This property of piezoelectric materials is well known and is classified as either hysteresis or "creep".
Sensitivity variation with voltage and hysteresis make it such that the position of the probe is not linear with the voltage applied to the electrodes on the piezoelectric material. Such non-linearity in probe position is transferred to, and therefore corrupts, the topographical data produced by the probe. In the prior art, several different methods exist which reduce the inaccuracies caused by the fundamental non-linearity of the scanner material. U.S. Pat. No. 5,051,646 to Elings et al. describes the use of a non-linear voltage profile (where each half-cycle of the former triangular wave has been replaced by the sum of a straight line and a decaying exponential). The key parameters of the non-linear function are the amplitude (Mag) and decay constant (Arg) of the exponential. These parameters are adjusted experimentally by the user, based on visual inspection of images and signal traces produced by the microscope. The microscope is then operated in an `open-loop` mode in which the control system drives the scanner using the pre-determined voltage profile; it is then assumed that the probe position varies linearly with time. Another method in the prior art involves fitting the scanner with position sensors, which may use optical, capacitive or strain transducers. The output of the position sensor is used in a `closed-loop` mode, that is, the controller adjusts the drive voltage so that the scanner motion conforms to the programmed trajectory. The accuracy of a closed-loop system depends on several assumptions, including: that the sensor output is linear in position (or that its non-linearity has been calibrated), that the frame of reference is stable, that sensor output on each axis is independent of the scanner position on the other axes, and that the Abbe error (due to the distance between the probe and the sensing point) can be neglected.
Although the above methods can provide a noticeable improvement in scan linearity (feature positions can be accurate to 1-5%), residual non-linearity can still be significant for many purposes. With advances in current technology and the strict engineering requirement of many current components, precise, accurate measurements of objects such as CD-ROM surfaces, magnetic films, microlithographic structures and biomaterials need to be made for quality control and to prevent undesired effects. For example, the new DVD (digital video disc) standard calls for a mean track pitch of 740 nm with a maximum allowable jitter (range) of .+-.30 nm. To achieve a range of .+-.30 nm, the standard deviation should be 10 nm or less. According to the gage-maker's rule, the measurement tool should be 4.times. more precise than the object being measured, so therefore a standard deviation of 2.5 nm is required. Current calibration methods for scanning probe microscopes cannot produce this measurement accuracy.
There is therefore a need for a method for calibrating a scanning probe microscope in order to remove non-linearity artifacts in the probe data caused by non-linear probe motion. The present invention is directed toward meeting this need.